308 primer problem?

I bought a Lee auto prime XR the other day. I have always used the press to install primers. Started priming some twice shot Winchester brass that had been tumbled sized and trimmed. I had some CCI # 34 primers and had some real difficulty with seating them. Anyone ever have this problem with these primers ? The primer pockets were cleaned with the the RCBS tool.

CCI primers tend to run a bit "fatter" than others, and this is quite common with them. I assume you're loading for a military rifle with a floating firing pin? Still, you might try another make (Rem 9 1/2, WLRs, whatever) just to see if that resolves the problem. If you're really worried about slam fires, just remember that the thicker cup of the #34 is offset by primers being seated high, which results in an even greater risk of slam fires. Make sure they're seated at least a few thou below the case head, and you reduce the risk of this happening quite a bit, regardless of the make of primer you're using.